Object 1 is moving along the x axis with an initial velocity +7 m/s, where the +

Question

Object 1 is moving along the x axis with an initial velocity +7 m/s, where the + sign indicates that it is moving to the right. As the drawing shows, object 1 collides with a second object that is initially at rest. The collision is not head-on, so the objects move off in different directions after the collision. The net external force acting on the two-object system is zero. After the collision, object 1 has a velocity of 5 m/s with the angle = 45° What is the velocity of object 2 after the collision? That is, the magnitude and the angle?

I understand that can easily be found by using 90° - 45° = 45°, but there should be a mathematical way using the tangent function. Please show and explain the steps to get and the velocity of object two after the collision.

Explanation / Answer

the momentum is conserved for the whole system. P=m1*7*i. after collision. P=-(m1*5*sin45-m2*v2*sin0)j+(m1*5*sin45+m2*v2*cos0)i. the two object have identical mass. so we cancel m1 and m2 out. we have. v2*sin0=5*sin45. 5*sin45+v2*cos0=7. from this we have tan0=5*sin45/(7-5*sin45) so that 0 = 45 degrees. ---------- plug in above equations. v2=5*sin45/sin45=5(m/s)

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